As per
the legend, Goddess Parvathi took the form of Kamadhenu (cow) and came to this
village. One day villagers here saw the cow pouring its milk by its own, on an
ant hill. They dissolved the ant hill to find a beautiful Shiva Lingam inside.
They installed the deity in the same place and formed this temple. As the cow
poured milk by itself on God, the place came to be known as Thiru Idai Churam,
and Goddess is called as Govardhana Ambigai (In Sanskrit ‘Go’ means cow).

Lord Shiva served Gnanasambandar with food:

Once
Gnanasambandar was walking toward Thiruporur and was resting under a tree. He
was hungry when the lord came to him in the guise of a cowherd (Edayan) and
offered him curd rice in a mud pot. The saint refused saying he must pray in a
Shiva temple and only then have his meal. The cow herd brought him to this
temple and the saint had a bath at the pond nearby and the cowherd vanished
into the sanctum when the saint realised who had directed him to the temple and
fed him. The name of the place was Thiru edai Churam (Shepherd who fed) which
has been corrupted as Thiruvadi Soolam.

Etymology:

Lord
came to the saint on his way and left on the way -Idai in Tamil. Hence,
Lord is praised as Idai Suranathar. Sambandar sang Pathigam-10
verses in praise of Lord. It is also said that this place got its name as this village
is surrounded by hills. In Thamizh, the place between hills is called “Churam”.

Gowthama Rishi worshipped Shiva here:

The Lord
here is also said to have been worshipped by an ancient sage called Gowthama
Rishi.

Ambica with back foot posture:

Lord Shiva
once set out to help child saint Tirugnanasambandar who was tired then. When
Ambica too joined Him, Lord asked her to be back as any child would recognize
the Mother who fed it. He will easily recognize both. Lord simply
wanted to go alone. As Ambica was ready to accompany the Lord, She
is seen ready to go walking with Lord, it is described. Those with
disfigured legs pray to Ambica.